▲support 后面通常接名词或代词作宾语，既不接不定式也不接动名词，你的两个句子可以翻译成（不一定要用 support）：
She speaks for [is for, is in favour of] protecting wildlife. 她支持保护野生动物。
Most people support military action. 大多数人支持采取军事行动。
▲其他表示“支持”的一些表达：
I wouldn’t be in favour of income tax cuts. 我不会支持削减所得税。
The management committee upheld her decision to fire two of her staff. 管理委员会支持她解雇两名员工的决定。
Deep down, she supported her husband’s involvement in the organization. 在心底里，她支持丈夫参加这个组织。
There is a very good argument for increasing spending on education. 有非常充足的理由支持增加教育支出。
I have to get five letters of recommendation to support my application to medical school. 为了支持我申请去医学院上学，我必须要有五封推荐信。